I was ironing at the weekend, so rewatched the entire series to date. I missed lots before, so apologies if this is really obvious or has already been said.
At the end of Episode one Baptiste declares that when Alice returned, he said "when she came back, she was not free - she was still a prisoner".
That combined with the fact that Alice confirms in Episode one her kidnapper had a German accent ( but we know DK is Scottish) the warning from the Brig in Episode 2 to keep her mouth shut, and her saying to the waiter that "she's taken" makes me think she was complicit in keeping the secret. So what would she value more than life / her freedom? I can only think it must be her child. I think the daughter is hers and she kept silent to protect her daughter. I also agree when she said Sophie in the ambulance, I think she was delirious and was telling them her name.
As for the three in Iraq, I wondered whether the three are Henry Reed / Brig and the Butcher's Wife (BW). When the Brig looks at the photo of Iraq in Episode three, it is very blurry on my to, but it does look like there's a black man and a woman there. When Daniel Reed came to see BW in the shop, she told him that she had a reputation and many people did not like her. Daniel tells her his dad wrote in his diary every day until Iraq... I wondered whether she was the third person involved and her husband was framed for the kidnapping because of her / her involvement in Iraq??
Im not sure if I'm reading too much into this, but in Episode 2 in 2016 Baptiste says "if we find Daniel Reed, we'll find those two girls". So does he think they're still alive? Given he knows about the one dead body in the shed, it's an odd thing to say. Also the Brig says when talking to Sam about Alice that he wondered what happened to Alice. Does this mean that she could still be alive? That he knew it wasn't her body in the shed.
Also, when Baptiste asks for a DNA test for Alice, the Brig shuts him down. So did he know Alice wasn't Alice, so could he have arranged the fake DNA to solve it? He knew the suspicions Baptiste had. So I wonder whether he's going to have a lot more involvement because everything seems to keep coming back to him.
Out of interest, Driller Killer was in the investigation when Alice first returned - so also able to change / fabricate evidence if needed.
Finally, there's something that we don't yet know about Sam. He's off duty because "what you did Sam was a cry for help" and whatever it is, it causes Matthew to hate Sam and blame him because at the grave Sam says "he's not forgiven me" so obviously Sam does something major to break down the relationship with Matthew, but we've not seen that yet. Don't think that's going to be connected to the disappearance though.
Anyway, just my musings...